Definition 2.22 (Def. 3.1 in [1]}) 
A Courant algebroid is a quadruple \((E, \langle \cdot ,\cdot \rangle , \rho , \llbracket \cdot ,\cdot \rrbracket )\) 
where:
\(E\rightarrow M\)  is a vector bundle,
\(\langle \cdot ,\cdot \rangle :\Gamma (E)\times \Gamma (E)\rightarrow C^{\infty }(M)\)  is a non-degenerate symmetric bilinear form,
\(\rho :E\rightarrow TM\)  is a bundle map called anchor, and
\(\llbracket \cdot ,\cdot \rrbracket : \Gamma (E)\times \Gamma (E)\rightarrow \Gamma (E)\)  is a bilinear operation called Dorfman bracket,
subject to the following axioms for all \(X,Y,Z\in \Gamma (E)\) :
